(1) For the following system of ODES: (i) First, convert the system into a matrix equation,...
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the solution if the initial values are x(0)(0)-y(0)0 and
2. (12 points) Write the ODEs as a 2 x 2 system and then find the general solution using the eigenvalues and eigenvectors of the constant (0) 9. matrix that appears in your system. Find the...
(1) For the following systems of ODEs, find the general solutions (in vector form), ygen. Make sure that your solutions only contain purely real vectors, i.e., the imaginary unit, '2', should not appear in your solutions. y1 = 2y2 y = -2y1 (b) { y = 8y1 - 9y2 y = 4y1 - 4y2 (a) { General Solution for (a): General Solution for (b):
vector x' = [ the first row is 2 and 8, the second row is -1 and -2] vector x (i) Compute the eigenvalues and eigenvectors of the system. (ii) Use the eigenvalues to classify the equilibrium type of the origin. (iii) Use the eigenvectors as guides to plot a phase portrait of the system. (iv) Present a general solution to the system of ODE. (v) Find the particular solution to this system of ODE if vector x(0) = [...
For the following system of first order difference equations xt+1=-xt-2yt +24 yt+1= -2xt+2yt+9 1) Present the system in matrix form. (2) Find the equilibrium vector. (3) Find the eigenvalues and eigenvectors for this system. (4) Find the general solution. (5) Plot the phase diagram.
Please answer all parts with full & clear solutions so I can
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2. Consider the following system of ordinary differential equations, 3 y1 (t) 4у (t) dy1 (t)/dt dy2 (t)/dt 4y2(t), 3 y2(t) with initial conditions yı(0) = 1, y2(0) = 0. (a) Write down the system of ordinary differential equations in matrix-vector form. You should also give the initial conditions in vector form. [2] [6] (b) Find exp(At), where A is the matrix you found in (a)....
(1 point) Consider the linear system -3 -2 333 5 a. Find the eigenvalues and eigenvectors for the coefficient matrix. di = and 12 02 b. Find the real-valued solution to the initial value problem syi ly -341 – 2y2, 5y1 + 3y2, yı(0) = 11, y2(0) = -15. Use t as the independent variable in your answers. yı(t) y2(t)
(1 point) Consider the linear system 3 2 ' = y. -5 -3 a. Find the eigenvalues and eigenvectors for the coefficient matrix. 2 = 15 and 2 V2 b. Find the real-valued solution to the initial value problem Syi ly 3y1 + 2y2, -541 – 3y2, yı(0) = 0, y2(0) = -5. Use t as the independent variable in your answers. yı(t) y2(t)
linear algebra
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal -1 0-1 0-1 0 - 1 0 9 1 Find the characteristic polynomial of A. |x - Al- Find the eigenvalues of A. (Enter your answers from smallest to largest.) (21, 22, 23) Find the general form for every eigenvector corresponding to 21. (Uses as your parameter.) X1 - Find the general form for every elge vector corresponding to Az. (Uset as your...
alue problem yn value) +13y=0, y(0)=3.y (0)-Owe use the To solve an initial v eigenvalue method. (Complex eigenvalue 1. I) Convert the equation into a first order linear system 2) Write the system in the matrix form: 3) Find the eigenvalues: 4) Find associated eigenvector(s): 5) Write the general solution of the system figure out the c and c2 To find the particular soluion 6) 2 7) Find the particular solution of the system 8) Write the particular solution of...
Problem 5. (1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. and iz = b. Find the real-valued solution to the initial value problem - -3y - 2y2 Syı + 3y2 yı(0) = -7, (0) = 10 Use I as the independent variable in your answers. Y() = Note: You can earn partial credit on this problem. Problem 6. (1 point) Find the most general real-valued solution to the linear system of differential...